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The estate of the girls’ late father, Matthew Badger, was suing the city and several officials claiming they were negligent in inspecting construction work on the home — then tried to cover up the cause of the blaze that took Lily, 9, and twins Grace and Sarah, 7, alongside the parents of their mother Madonna by demolishing the fire-ravaged house before a proper investigation could take place.

The parties resolved the matter “without reflecting any liability or fault on the part of the defendants,” according to the city’s top eagle.

“The parties consider the settlement to be fair,” Legal Affairs Director Kathryn Emmett wrote in a statement, per The Hour.

“The city is sympathetic to the tremendous losses suffered by the Badger family. Understanding the family’s concern that the demolition of the house prevented them from being able to conduct their own investigation of the cause of the fire, the city has agreed to address the circumstances under which a fire-ravaged home can be demolished.”

Badger’s brother, who was administering the case after the bereaved dad passed away himself in February, also expressed relief that the legal battle had come to an end.

“I appreciate that the Stamford defendants have agreed to resolve this case,” Cambell Badger said in a statement. “This has been a great ordeal for my brother, for Madonna Badger, and for my entire family.”

In addition to the undisclosed payout, the city will contribute $250,000 to fund a scholarship at a school or charity that will recognize the three girls, the paper reports.

Matthew Badger had previously won a total of $7 million against the contractors Madonna had hired to renovate the 116-year-old Stamford mansion.